{
  "id": "1008.1469",
  "version": "v2",
  "published": "2010-08-09T09:01:45.000Z",
  "updated": "2011-04-05T12:50:35.000Z",
  "title": "A q-analogue of some binomial coefficient identities of Y. Sun",
  "authors": [
    "Victor J. W. Guo",
    "Dan-Mei Yang"
  ],
  "comment": "6 pages, final version",
  "journal": "Electron. J. Combin. 18 (1) (2011), #P78",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a $q$-analogue of some binomial coefficient identities of Y. Sun [Electron. J. Combin. 17 (2010), #N20] as follows: {align*} \\sum_{k=0}^{\\lfloor n/2\\rfloor}{m+k\\brack k}_{q^2}{m+1\\brack n-2k}_{q} q^{n-2k\\choose 2} &={m+n\\brack n}_{q}, \\sum_{k=0}^{\\lfloor n/4\\rfloor}{m+k\\brack k}_{q^4}{m+1\\brack n-4k}_{q} q^{n-4k\\choose 2} &=\\sum_{k=0}^{\\lfloor n/2\\rfloor}(-1)^k{m+k\\brack k}_{q^2}{m+n-2k\\brack n-2k}_{q}, {align*} where ${n\\brack k}_q$ stands for the $q$-binomial coefficient. We provide two proofs, one of which is combinatorial via partitions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-05T12:50:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A10",
      "05A17"
    ],
    "keywords": [
      "binomial coefficient identities",
      "q-analogue",
      "combinatorial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1469G"
    }
  }
}